Hydrogeology Journal

, Volume 21, Issue 1, pp 185–200

Sensitivity analysis of lake mass balance in discontinuous permafrost: the example of disappearing Twelvemile Lake, Yukon Flats, Alaska (USA)

  • S. M. Jepsen
  • C. I. Voss
  • M. A. Walvoord
  • J. R. Rose
  • B. J. Minsley
  • B. D. Smith
Paper

DOI: 10.1007/s10040-012-0896-5

Cite this article as:
Jepsen, S.M., Voss, C.I., Walvoord, M.A. et al. Hydrogeol J (2013) 21: 185. doi:10.1007/s10040-012-0896-5

Abstract

Many lakes in northern high latitudes have undergone substantial changes in surface area over the last four decades, possibly as a result of climate warming. In the discontinuous permafrost of Yukon Flats, interior Alaska (USA), these changes have been non-uniform across adjacent watersheds, suggesting local controls on lake water budgets. Mechanisms that could explain the decreasing mass of one lake in Yukon Flats since the early 1980s, Twelvemile Lake, are identified via a scoping analysis that considers plausible changes in snowmelt mass and infiltration, permafrost distribution, and climate warming. Because predicted changes in evaporation (2  cmyr−1) are inadequate to explain the observed 17.5 cmyr−1 reduction in mass balance, other mechanisms are required. The most important potential mechanisms are found to involve: (1) changes in shallow, lateral groundwater flow to the lake possibly facilitated by vertical freeze-thaw migration of the permafrost table in gravel; (2) increased loss of lake water as downward groundwater flow through an open talik to a permeable subpermafrost flowpath; and (3) reduced snow meltwater inputs due to decreased snowpack mass and increased infiltration of snowmelt into, and subsequent evaporation from, fine-grained sediment mantling the permafrost-free lake basin.

Keywords

Geophysical methods Groundwater recharge/water budget Groundwater/surface-water relations Permafrost Alaska (USA) 

Analyse de sensibilité du bilan d’eau d’un lac dans un permafrost discontinu : l’exemple de la disparition de Twelvemile Lake, Yukon Flats, Alaska (USA)

Résumé

De nombreux lacs de haute latitude Nord ont subi des changements substantiels de surface au cours des quatre dernières décades, peut être comme résultat du réchauffement climatique. Dans le permafrost discontinu de Yukon Flats, Alaska intérieur (USA), ces changements ont été non uniformes de part et d’autre de lignes de partage des eaux, ce qui suggère un contrôle local des budgets eau des lacs. Des mécanismes qui pourraient expliquer la décroissance du volume d’un lac sur Yukon Flats depuis le début des années 1980, Twelvemile Lake, ont été identifiés par une analyse étendue qui considère des changements plausibles de la masse de neige fondue et de l’infiltration, distribution du permafrost et réchauffement climatique. Parce que les changement d’évaporation prévus (2 cm/an,) sont non adéquats pour expliquer la réduction de 17.5 cm/an du bilan massique, d’autres mécanismes sont requis. Les mécanismes potentiels les plus importants trouvés incluent: (1) changements dans le flux de nappe superficiel latéral vers le lac éventuellement facilités par une migration gel-dégel de la surface du permafrost dans le gravier; (2) perte accrue de l’eau de lac par flux descendant à travers un talik ouvert vers un chenal perméable sous le permafrost; et (3) recharge réduite par eau de fusion de neige due à la décroissance de la masse du pack neigeux et infiltrations accrue de neige fondue, et évaporation subséquente depuis le manteau de sédiment à grain fin couvrant le bassin du lac libre de permafrost.

Análisis de sensibilidad del balance de masa de un lago en un permafrost discontinuo: el ejemplo del desaparecido lago Twelvemile, Yukon Flats, Alaska (EEUU)

Resumen

Muchos lagos en las altas latitudes nórdicas han experimentado cambios sustanciales en su extensión superficial durante las últimas cuatro décadas, posiblemente como resultado del calentamiento climático. En el permafrost discontinuo de Yukon Flats, en el interior de Alaska (EEUU), estos cambios no han sido uniformes a través de cuencas adyacentes, lo que sugiere controles locales sobre los balances de agua del lago. Los mecanismos que podrían explicar la disminución de la masa en uno de los lagos en Yukon Flats desde los comienzos de 1980, el Lago Twelvemile, se identifican a través de un análisis de observación que considera cambios plausibles en la masa de nieve derretida e infiltración, en la distribución del permafrost y en el calentamiento climático. Debido a que los cambios predichos en la evaporación (2 cm yr−1) son inadecuados para explicar la reducción de 17.5 cm yr−1 observada en el balance de masa, se requieren otros mecanismos. Se encontró que los mecanismos potenciales de mayor importancia involucraban: (1) cambios en el flujo lateral de agua subterránea somera hacia el lago posiblemente facilitado por una migración vertical del nivel del permafrost en las gravas debido a procesos de congelamiento – descongelamiento; (2) incremento de la pérdida del agua del lago como flujo subterránea descendente a través de un talik abierto hacia una trayectoria de flujo en un subpermafrost permeable; y (3) entradas reducidas de agua del derretimiento de nieve debido a una reducción de la masa de la capa de nieve y un aumento de la infiltración de la nieve derretida y subsecuente evaporación hacia los sedimentos de grano fino que recubren la cuenca del lago libre de permafrost.

不连续永冻区湖水质量平衡敏感性分析:以美国阿拉斯加州育空河平原Twelvemile湖消退为例

摘要

北部高纬度地区的很多湖泊在过去的四十年里经历了可能是由于气候变暖引起的实质性面积变化。在美国阿拉斯加州育空河平原的不连续永冻层,这些变化非均匀地横穿邻近流域,表明对湖水平衡的局部调控。通过考虑貌似可信的融雪水质量、入渗、永冻层分布和气候变暖的变化的域分析,识别能够解释始于80年代早期的育空河平原Twelvemile湖水量减少的机制。因为预测的蒸发量(每年2 cm)变化不足以解释观测到的质量平衡上每年17.5 cm的减少,故存在其他机制。本文发现的潜在重要机制包括:(1)砂砾石中永冻土面的垂向冻融迁移有助于流向湖泊的浅层和侧向地下水径流变化;(2)由于地下水向下流经开放的融区而到达可渗透的永冻层,湖水损失水量增加;(3)由于积雪量减少而入渗的融雪量增加,湖泊融雪量的输入项减少,且随后在细粒的沉积物覆盖的沉积盆地永冻层上发生蒸发。

Análise de sensibilidade do balanço de massa de lagos no permafrost descontínuo: o exemplo do desaparecimento do Lago Twelvemile, Yukon Flats, Alasca (EUA)

Resumo

Muitos lagos situados nas altas latitudes do norte sofreram alterações substanciais na sua área de superfície ao longo das últimas quatro décadas, possivelmente em consequência do aquecimento climático. No permafrost descontínuo de Yukon Flats, no interior do Alasca (EUA), estas alterações têm ocorrido de forma não-uniforme entre bacias hidrográficas adjacentes, sugerindo a existência de fatores locais que controlam os balanços hídricos dos lagos. Identificam-se aqui os mecanismos que poderiam explicar o decréscimo de massa de um lago em Yukon Flats, o Lago Twelvemile, desde o início dos anos 80, através de uma análise abrangente que considera a existência de alterações plausíveis na massa do degelo e na infiltração da água, na distribuição do permafrost e o efeito do aquecimento climático. Uma vez que as mudanças previstas na evaporação (2 cm ano−1) são insuficientes para explicar a redução de 17.5 cm ano−1 observada no balanço de massa do lago, é necessário existirem outros mecanismos. Os mecanismos potenciais mais relevantes parecem envolver: (1) mudanças no escoamento subterrâneo lateral pouco profundo, facilitado possivelmente pela migração vertical da frente de congelamento no permafrost em cascalho, (2) o aumento das perdas de água do lago através da percolação subterrânea ao longo de um talik (local onde o solo não está congelado), até chegar a um caminho de fluxo no subpermafrost permeável, e (3) uma redução das entradas de água do degelo, devido à diminuição da massa acumulada de neve e por causa do aumento da infiltração da água do degelo, e consequente evaporação a partir dos sedimentos finos que existem na parte da bacia do lago livre de permafrost.

Introduction

Many lakes in interior Alaska (Rover et al. 2012; Riordan et al. 2006; Yoshikawa and Hinzman 2003) and Siberia (Smith et al. 2005) have undergone substantial changes in surface area over the last four decades. These changes have not been uniform among watersheds, suggesting the importance of local, watershed-scale processes that currently are not well understood. Such non-uniformity in the surface area changes of lakes has been documented in the Yukon Flats basin of interior Alaska (Rover et al. 2012; Riordan et al. 2006), a region underlain by discontinuous permafrost. Discontinuous permafrost, defined as “permafrost occurring in some areas beneath the exposed land surface throughout a geographic region where other areas are free of permafrost” (van Everdingen 1998), forms an environment where surface water and groundwater are interconnected only through unfrozen conduits (taliks; Michel and van Everdingen 1994; van Everdingen 1990), and where the infiltration capacity of frozen soil can exhibit high spatial variability (Carey and Woo 1999; Ford and Bedford 1987; Dingman 1975).

During the last four decades, high latitudes have undergone an abrupt increase in air temperature (Wendler and Shulski 2009; Barber et al. 2004) and a shortening in the spring duration of snowcover (Brown et al. 2010; Foster et al. 2008). The effect of these changes on the water balance of lakes in Yukon Flats is not thoroughly understood, including the role of permafrost thaw. This stems from the complexity of permafrost thaw processes (Jorgenson and Osterkamp 2005) and associated interactions with lake recharge. For effective planning and conservation of land and water resources in Yukon Flats, more understanding is needed about the relative significance of different hydrological pathways to and from northern lakes and how changes in climate and permafrost will affect these pathways. Such enhanced understanding may also provide insights into the mechanisms of increasing groundwater discharge to rivers in this region (Walvoord and Striegl 2007; Lyon and Destouni 2009).

The goal of this study is to identify climate-related mechanisms that could account for the observed volume changes of lakes in Yukon Flats. The analysis is carried out by testing the sensitivity of lake volume, in an area of detailed study, to assumed changes in different plausible water flowpaths, herein defined as a “scoping analysis.” The effect of climate, between 1950 and 2010, on the mechanisms considered are both direct (evaporation, snow/rain partitioning) and indirect (configuration of permafrost). The lake selected for study is Twelvemile Lake, located 18 km southwest of Fort Yukon, Alaska, chosen because of (1) its substantial reduction (∼60 %) in surface area since the early 1980s (Rover et al. 2010; M.T. Jorgenson, Alaska Ecoscience, unpublished data, 2010) and (2) the nonuniformity displayed between Twelvemile Lake and a neighboring lake, 2 km to the southeast, which has shown no apparent change in surface area since the early 1950s (hereafter “Buddy Lake”). The findings of this study provide a short list of potentially important mechanisms that could be analyzed in greater detail.

Study area

Twelvemile Lake is located in the boreal region of interior Alaska, in the northern zone of discontinuous permafrost (Brown et al. 1998; Jorgenson et al. 2008), in a 9.8-km2 watershed (Fig. 1a). The lake currently measures about 1.2 km across, has a maximum depth of about 10 m (Anderson et al. 2010), and has a surface elevation of about 127 m based on the National Elevation Dataset (NED) 2-arcsecond digital elevation model (DEM; Gesch 2007). The Yukon River arcs around Twelvemile Lake to the north, ranging in elevation from about 135 m above sea level (asl), 17 km east of the lake, to an elevation of about 120 m, 17 km northwest of the lake (NED 2-arcsecond DEM, Gesch 2007). Numerous channels without perennially flowing water form topographic thresholds along the watershed boundary of Twelvemile Lake (e.g., inlet and outlet channels in Fig. 1a). Slopes in the watershed are gentle (∼1 %), at elevations ranging from 127 to 142 m asl. Mean annual air temperature and precipitation in Fort Yukon, located 18 km northeast of Twelvemile Lake, are about −6°C and 0.17 m, respectively (Nakanishi and Dorava 1994), and the thickness of permafrost in this area is reported to be 90–130 m (Minsley et al. 2012; Clark et al. 2009; Williams 1962). The top of the permafrost in the Twelvemile Lake watershed has been observed at depths ranging from 0.4 to 2.5 m (Jepsen et al. 2012).
Fig. 1

General topographic features and sediment characteristics of the study area. a Topographic map of the Twelvemile Lake watershed, Alaska. Elevations are based on a 2.5-m-resolution LIDAR DEM (Gesch 2007). The boundary of Buddy Lake during 1984 is similar to that in 2010 and thus is not shown. b Schematic cross-section view of sediment textures and permafrost distribution; triangles denote lake margin locations in the given years (1984 and 2010). Line AA′ is shown in panel a (See also Minsley et al. 2012)

Vegetation in the Twelvemile Lake watershed follows a successional sequence (Chapin et al. 2006) of sedge and grass meadows in the low-lying areas most recently under water, grading upward in elevation into deciduous forests of willow, balsam poplar, aspen and birch near the early 1980s lake margin, and grading further upward into the oldest perennial forests of white spruce. The deciduous and perennial forests equally comprise roughly 60 % of the terrestrial watershed area, and the remaining 40 % consists of meadows and bare soil (Fig. 2b, c). Spruce forest is more abundant around Buddy Lake than Twelvemile Lake (Fig. 2b, c).
Fig. 2

(a--c) Images of Twelvemile and Buddy Lakes between 1952 and 2011 and (d) time series of lake surface elevation, with trend and p-value (two-tail) shown in parentheses. Image (c) is from Landsat 5 TM, others are documented in Table 1

Near-surface mineral soil in the Twelvemile Lake watershed consists of “sand/gravel,” approximately 50 m in thickness (Minsley et al. 2012), consisting of silt and sand overlying fluvial gravel (Fig. 1b). The thickness of the upper silt and sand varies from 0 to 0.3 m in the inlet and outlet channels near the watershed margin, to about 4 m near the present lake margin (M.T. Jorgenson, Alaska Ecoscience, personal communication, 2011; Jepsen et al. 2012). In exposed areas covered by the early 1980s lake, the silt and sand is interspersed with limnic material, and permafrost is generally absent (Jepsen et al. 2012; Minsley et al. 2012). Permafrost appears to be more discontinuous in the inlet and outlet channels than in the forested uplands. The silt, sand and limnic material overlying gravel is referred to as “loam” for the hydrological calculations. The sand/gravel appears to correspond to the Pleistocene “alluvial fan and related terrace deposits” of the Yukon River (Williams 1962). Lacustrine deposits of silt and silty sand (“silt/silty sand”) are believed to underlie the sand/gravel (Minsley et al. 2012; Williams 1962; Fig. 1b). A surface mantle of terrestrial organic material ranges in thickness from less than 0.1 m in the white spruce forest, where it is predominantly moss, to thicker sequences (reaching 0.5 m) of hemic and sapric organics in the low-lying channel features near and outside of the early 1980s lake margin. Soil types around Buddy Lake are thought to be similar to those around Twelvemile, though observations in the former are limited (data available in Jepsen et al. 2012).

Methods

Summary

Water fluxes to and from Twelvemile Lake are estimated via a scoping analysis for variable partitioning of precipitation between snow and rain, different flowpaths of snowmelt, and historic changes in growing season air temperature (May–September). The past and present spatial distribution of permafrost, which acts as an aquiclude, at the spatial scale necessary for this study is not completely known; therefore, a variety of permafrost configurations and associated flow pathways are considered in order to address different plausible boundaries of the hydrologic system. Some water fluxes to/from the lake occur directly from the atmosphere (“direct flux”), while other fluxes occur indirectly as groundwater or overland flow (“indirect flux”). Direct fluxes are defined to be snow, rainfall, and lake evaporation. Indirect fluxes (Qi) are enumerated as follows (Fig. 3): (1) flows from the contributing-area slopes of the watershed (Qcontrib, L3 T−1), (2) subsurface flow across the watershed boundary over a “low spot” (“threshold”) formed by a topographically depressed permafrost table (Qthresh, L3 T−1), and (3) flows to or from the lake through an open talik (Qtalik, L3 T−1). Indirect fluxes are determined based on the hydraulic forces and hydraulic properties along multiple assumed flowpaths. The spatial distribution of land features and water-surface elevations are determined using aerial photos and satellite images (Table 1) and a LIDAR 2.5-m-resolution DEM (Gesch 2007). Constraints on the current spatial distribution of permafrost and water-table elevation are determined from augering and frost probing during 2010 and 2011. Mapped resistivity from an airborne electromagnetic survey (AEM) conducted during 2010 helped to visualize the overall pattern of ground ice in the watershed (Minsley et al. 2012; Ball et al. 2011; Abraham 2011).
Fig. 3

Conceptual model of water fluxes considered in this study. a View looking northeast, perpendicular to the inlet and outlet channels, b view looking northwest. P liquid precipitation falling on the lake, SWE meltwater from snow that has fallen on the lake, E lake evaporation

Table 1

Aerial photos and satellite images used to determine historical lake elevation

Date (yyyy/mm/dd)

Source information

Reference

1952/06/20

ID# BM06160110209

USGS (1974)

1955/05/10

ID # BM00040030216

USGS (1974)

1966/08/16

ID # DS1036-1099DA019

USGS (1995)

1969/09/23

ID # DS1052-1017DA039

USGS (1995)

1975/07/07

ID # DZB1210-500119 L007001

USGS (2005)

1978/07/12

ID # 6386002500130

USGS (1974)

1984/06/18

Landsat 5 TM

USGS (2010)

1985/09/25

Landsat 5 MSS

USGS (2010)

1989/07/10

Landsat 4 TM

USGS (2010)

1999/06/28

Landsat 5 TM

USGS (2010)

1999/07/14

Landsat 5 TM

USGS (2010)

1999/09/24

Landsat 7 ETM+

USGS (2010)

2001/06/25

Landsat 7 ETM+

USGS (2010)

2001/07/27

Landsat 7 ETM+

USGS (2010)

2001/08/28

Landsat 7 ETM+

USGS (2010)

2001/09/29

Landsat 7 ETM+

USGS (2010)

2003/05/30

Landsat 7 ETM+

USGS (2010)

2003/08/10

Landsat 5 TM

USGS (2010)

2003/10/05

Landsat 7 ETM+

USGS (2010)

2007/05/25

Landsat 7 ETM+

USGS (2010)

2007/06/10

Landsat 7 ETM+

USGS (2010)

2007/08/29

Landsat 7 ETM+

USGS (2010)

2010/05/17

Landsat 7 ETM+

USGS (2010)

2010/06/02

Landsat 7 ETM+

USGS (2010)

2010/08/29

Landsat 5 TM

USGS (2010)

2010/09/22

Landsat 7 ETM+

USGS (2010)

Time periods of 1950–1980 and 1980–2010 are considered, the former period assumed to represent conditions prior to onset of lake lowering beginning in the early 1980s. Years 1984 and 2010 are used to represent lake geometries during the earlier and latter periods, respectively. Here, an indirect flux is defined to be “significant” if it alone provides at least half of the indirect flux required to produce the observed average rate of lake level change between 1950 and 2010. The lake water budget is considered to have “significant sensitivity” to change in a particular water flux if that change would produce at least half of the observed change in lake lowering beginning in the early 1980s. The methods are further detailed in the following.

Observations of permafrost and water table

An airborne electromagnetic (AEM) survey was flown over a 300-km2 grid encompassing Twelvemile Lake to measure subsurface electrical resistivity (Minsley et al. 2012; Ball et al. 2011; Abraham 2011), the goal being to map permafrost at depth based on its resistive nature relative to unfrozen ground. The study described here utilizes the geophysical inversion results of this survey, consisting of a resistivity grid of the upper 10 m (6 resistivity layers, thickness-weighted-average) and a resistivity cross section. Depths to permafrost were measured during September 2010 and August 2011 using a hand auger with 3-inch (7.6 cm) bucket, and frost probe (46 and 11 measurements, respectively). Water-table depths were measured from auger holes during August 2011 (data available in Jepsen et al. 2012). Observed depths to permafrost are superposed on the resistivity grid in order to compare datasets and make inferences about the spatial distribution of permafrost.

Climate data

Air temperature and precipitation records are used from two stations in Fort Yukon (Table 2, Fig. 4). Maximum snow water equivalent (SWE) is varied in the flow calculations for Qcontrib, with the sum of rain (May–September) and SWE assumed to remain constant. This assumption is consistent with statistically insignificant trends in total precipitation observed in interior Alaska (Wendler and Shulski 2009). SWE was estimated by multiplying the maximum snow thickness by a specific gravity value of 0.21 for taiga snow (Sturm et al. 2010, 2011). Maximum snow thickness data are not available prior to 2003; however, annual snowfall totals are available back to 1950 and are used to infer plausible changes in SWE (Table 2, Fig. 4c).
Table 2

Climate data from Fort Yukon, Alaska. No data available from 1991 to 2002. SD standard deviation of mean values over the period indicated, N number of years with data. Annual data are plotted in Fig. 4. Post-1990 air temperatures are from NCDC (1999), other post-1990 climate parameters are from NRCS (2011)

Monthly air temperature averages (°C)

 

1950–1980a

1980–2010a

Month

Mean

SD

N

Mean

SD

N

  May

6.6

1.6

16

8.5

1.6

11

  Jun

15.1

1.4

17

16.4

0.9

10

  Jul

16.5

1.2

15

17.7

0.9

9

  Aug

13.0

1.6

14

13.5

1.3

10

  Sep

4.8

1.1

15

5.6

2.0

11

  May–Sep mean

11.2

  

12.3

  

 

Annual snowfall (cm)

 

1950–1980a

1980–2010a, b

 

Mean

SD

N

Mean

SD

N

 

112.1

29.1

11

73.4

20.2

8

 

May–September precipitation totals (cm)

 

1950–1980a

1980–2010a, b

 

Mean

SD

N

Mean

SD

N

 

10

3.8

13

10

2.6

12

 

Maximum snow thickness (cm), years 2003–2010b

 

Mean

SD

N

   
 

46

8.9

8

   

References:

aWBAN station No. 26413 (NCDC 1999), data available for years 1922–1990, 2003–2010

bSNOTEL station No. 961 (NRCS 2011), data available for years 2002–2010.

Fig. 4

Historical climate observations at Fort Yukon, including a May and b July air temperature, c annual snowfall, and d May–September precipitation. Dashed lines indicate 1950–1980 and 1980–2010 averages used in this study. Values inside parentheses, upper-right corner of panels, are 1922–2010 trend and p-value (two-tail), respectively. Trend and p-value for June, August and September air temperature (not shown) are (0.022 °C yr−1, 0.009), (0.010 °C yr−1, 0.2), and (0.002 °C yr−1, 0.8), respectively. Gaps represent unavailable data. See Table 2 for meteorological station information

Lake surface elevation

Lake-surface elevations are determined by manually extracting lake-boundary elevations from georeferenced aerial photos, satellite images (Table 1), and the LIDAR elevation map in ArcGIS (20 recordings averaged at each date). The standard error of the mean elevation at each date ranged from 0.01 to 0.09 m (mean 0.02) for Twelvemile Lake, and 0.01 to 0.03 m (mean 0.02) for Buddy Lake. The LIDAR data were collected between July and September of 2009, and have a horizontal and vertical accuracy of 1.15 and 0.10 m, respectively. The LIDAR data reflect the surface elevation of water bodies, not bathymetry; therefore, only water-surface elevations higher than their 2009 levels could be observed.

Evaporation and precipitation (E, PET, SWE, P)

Lake evaporation (E) and potential evapotranspiration (PET) were estimated using the Thornthwaite equation (Thornthwaite 1948) and air temperatures in Table 2. Federer et al. (1996) showed that for the Fairbanks, Alaska, climate during 1961, PET predicted using the Thornthwaite equation is within about 16 cm yr−1 of values predicted using other methods that account for different landcover types.

Snowmelt occurs over a period of about 2–3 weeks in Fort Yukon—SNOTEL [SNOw TELemetry] Station No. 961, NRCS (2011)—which is an order of magnitude shorter than the rain season (May–September). Therefore, water flux to soil is divided into a component from SWE and a component from liquid precipitation (P), the latter assumed to occur uniformly between May and September. This assumption is a source of error; however, most rainfall in this arid, flat region is expected to infiltrate into and replenish soil moisture of the unfrozen loam of the active layer (e.g., Woo and Steer 1983; Woo et al. 1983).

Indirect fluxes to lake (Qi)

Lateral shallow groundwater flow across watershed boundary

Qthresh is the subsurface flux of water across the watershed boundary over an area of topographically depressed (i.e., “threshold”), or absent, permafrost (Fig. 3a). Such thresholds are envisioned to occur below the topographic lows in inactive channels along the watershed boundary. Flowpaths are considered following the Twelvemile Lake inlet channel connected to Buddy Lake, and the Twelvemile Lake outlet channel to a pond, as a function of threshold elevation (hth) in order to constrain possible flux magnitudes. If the threshold elevation becomes lower than the surface elevation of the adjacent water body in the downflow direction (“water body DF”), the flow process changes from spill-over type flow to channelized type flow. For flow from a lake, it is assumed that the water-table slopes down from that lake to the threshold as long as the threshold is higher in elevation than the surface of water body DF (Table 3). If the threshold elevation is lower than the surface of water body DF, a linear slope in water table is assumed between the lake and water body DF and a lower boundary of flow given by the threshold elevation (Table 3). Flow rates (m3 yr−1) are determined using the Dupuit equation:
Table 3

Constraints and relations used in the calculations of the Qthresh and Qcontrib water fluxes. Parameters are defined in the text and Table 4

Qthresh, lateral groundwater flow across watershed boundary over threshold

Flow direction

Threshold condition

Applicable relations

To Twelvemile Lake

hth < hl

Δhu = hbhth, Δhd = hlhth

 

hth ≥ hl

Δhu = hbhth, Δhd = 0

From Twelvemile Lake

hth < hp

Δhu = hlhth, Δhd = hphth

 

hth ≥ hp

Δhu = hlhth, Δhd = 0

 

Qcontrib, flow from slopes of watershed contributing area

Contributing area

Flowpath

Aquifer materials

Assumptions

Constraints in Eq. 4

Variable in Eq. 4

Outer (k = 0)

Minimum infiltration depth

Loam, fine sand, organic, snowpack

Snowmelt infiltrates to minimum depth for accommodation of meltwater volume.

y0 = ΔVin,0⋅(2⋅Ac,0ϕ)−1, dwt = y0

δt0

Outer (k = 0)

Maximum infiltration depth

Loam, fine sand

Snowmelt infiltrates to maximum depth (permafrost table).

δt0 = 5/12, dwt = ypy0

y0

Outer (k = 0)

Maximum infiltration depth

Gravel

Snowmelt infiltrates to maximum depth (permafrost table).

y0 = ΔVin,0⋅(2⋅Ac,0ϕ)−1, dwt = ypy0

δt0

Inner (k = 1)

No infiltration to gravel

Loam, fine sand, snowpack

No recharge of gravel aquifer, all water infiltrated is removed the same year by groundwater flow and/or evaporation.

y1 = ΔVin,1⋅(2⋅Ac,1ϕ)−1, dwt = y1

δt1

Inner (k = 1)

Infiltration to gravel

Gravel, coarse sand

Snowmelt and groundwater from outer area infiltrates and recharges gravel aquifer.

θw,1 = ΔVin,1⋅(Ac,1Lrϕ)−1, dwt = 0.5⋅Lr⋅(θgθw,1)

δt1

$$ {Q_{thresh}} = \frac{1}{2}{K_g}{w_{th}}\frac{{\Delta h_u^2 - \Delta h_d^2}}{{{L_{th}}}}{t_{spy}} $$
(1)
where Kg is the assumed hydraulic conductivity of gravel, 10−2 m s−1 (Freeze and Cherry 1979), wth is the assumed flow width, Δhu and Δhd are the flow thicknesses on the upflow and downflow sides of the threshold, respectively, Lth is the horizontal distance between locations of thickness Δhu and Δhd, assumed equal to the typical horizontal distance between the adjacent waterbodies, and tspy is a unit conversion factor. The parameter values and relations are provided in Tables 3 and 4.
Table 4

Parameter values used in the hydrological calculations

Symbol

Description

Value(s)

Al

Area of Twelvemile Lake (× 106 m2)

Year 1984: 3.1, year 2010: 1.2

Ashed

Area of Twelvemile Lake watershed (× 106 m2)

9.8

Ac,k

Area of contributing area k (× 106 m2)

Ac,0 = 6.7, Ac,1 = 1.9

At,j

Cross sectional area of segment j groundwater flow through open talik (× 106 m2)

At,3 = Al (3.1 for year 1984, 1.2 for year 2010), other terms variable

dwt

Depth to water table (m)

Variable

h

Water-body surface elevations: Twelvemile Lake = hl, Buddy Lake = hb, pond in outlet = hp (m)

Year 1984: hb = 132.5, hl = 130.2, hp = 129.5

Year 2010: hb = 132.5, hl = 126.8, hp = 128.6

hr

Reference elevations for Qtalik calculations

120.0 (Yukon R., N41°W from Twelvemile L.), 149.3 (Yukon R., S57°E from Twelvemile L.)

K

Saturated hydraulic conductivity (m s−1)

Loam: 10−5 [a], fine sand: 10−4 [a], organic soil: 10−3 [b], coarse sand: 10−3 [a], gravel: 10−2[a], snowpack: 10−1 [c]

Kt,j

K-value of segment j for Qtalik calculations (× 10−6 m s−1)

Kt,1 = 1 (silt), Kt,3 = 1 (silt), Kt,2 variable

Lth

Horizontal distance between water bodies for Qthresh calculations (× 103 m)

1.5

Lk

Inner perimeter, area k (× 103 m)

L0 = 9.5, L1 = 4.7

Lp

Lake perimeter (× 103 m)

Year 1984: 9.5, year 2010: 4.7

Lr

Radial distance across inner contributing area (m)

375 (computed using circles of equivalent areas)

Lt,j

Length of segment j for Qtalik calculations (× 103 m)

Lt,1 = 0.1; Lt,2 = 20.3 (Yukon R., N41°W from Twelvemile), 49.1 (Yukon R., S57°E from Twelvemile), 5.0 (Buddy Lk); Lt,3 = 0.1

P

Liquid precipitation during May–Sep [m⋅(5 month)−1]

Constrained by P + SWE = 0.2 (constant)

SWE

Maximum snow water equivalent (m yr−1)

Constrained by P + SWE = 0.2 (constant)

tspy

Unit conversion factor to seconds per year (s yr−1)

3.2 × 107

wth

Width of flow over threshold

75 m (AEM grid cell dimension)

yk

Vertical thickness of aquifer, area k (m)

y1 = 50

yp

Modeled mean depth to permafrost (m)

1.5

ϕ

Aquifer porosity

Mineral soil: 0.35 [a], organic soil: 0.85 [b], snowpack: 0.8 [d]

θg

Ground-surface slope (vertical/horizontal)

0.01

θw,k

Water-table slope, area k (vertical/horizontal)

θw,0 = 0.01

References:

aFreeze and Cherry (1979)

bLetts et al. (2000)

cSingh and Singh (2001)

dDetermined assuming a specific gravity of 0.21 for taiga snow (Sturm et al. 2010, 2011)

Vertical groundwater flow through open talik

Qtalik is the groundwater flow to or from Twelvemile Lake through an open talik (m3 yr−1) to a receiving or losing surface-water body, assumed to follow a path consisting of three segments: a vertical path through an open talik between Twelvemile Lake and the underside of permafrost (segment 1, j = 1), a horizontal path below permafrost (j = 2), and a vertical path between the underside of permafrost and a receiving or losing water body (j = 3). Flow rates are calculated assuming Darcy’s Law for three flow segments in series:
$$ {Q_{talik}} = \frac{{{h_r} - {h_l}}}{{\sum\limits_{j = 1}^3 {{{\left( {{C_{t,j}}} \right)}^{ - 1}}} }}{t_{spy}} $$
(2)
where Ct,j is the hydraulic conductance along flow segment j, defined as Kt,jAt,j⋅(Lt,j)−1, where Kt,j, At,j and Lt,j are the saturated hydraulic conductivity, cross-sectional area and length of segment j, hl is lake elevation, and hr the reference elevation of the connecting water body (values in Table 4). Because of the low conductance values observed for the subpermafrost path (i.e., Lt,2 >> Lt,1, Lt,2 > > Lt,3), flow rates are determined for different values of Kt,2At,2 (similar to segment 2 transmissivity), as a function of talik area (At,1 = “Atalik”). The following endmember cases are considered: (1) maximum flow from Yukon River (S 57° E from Twelvemile), (2) maximum flow to Yukon River (N 41° W from Twelvemile), and (3) flow from Buddy Lake to Twelvemile. River elevations and horizontal distances in Table 4 are from the 2 arc-second NED DEM.

Lake recharge from snowmelt

Qcontrib is the water flux to Twelvemile originating from slopes of the watershed contributing area (as overland and subsurface flow). The quantity reaching the lake is equal to the quantity delivered to the contributing area, minus that which evaporates. The quantity that evaporates is dependent on both the rate and depth of flow (Quinton et al. 2009; Suzuki et al. 2006; Slaughter and Kane 1979; Dingman 1975). Determination of the sensitivity of Qcontrib to the flowpath and volume of snowmelt is the objective of this calculation. Different flowpaths are tested to represent different frost-table depths and amounts of snowmelt infiltration into mineral soil (Quinton et al. 2009; Granger et al. 1984; Woo et al. 1983; Kane and Stein 1983). Values of saturated hydraulic conductivity (K) and hydraulic potential gradient are dependent on the assumed flowpath. High K-values represent fast overland flow (modeled as the “snowpack” aquifer); low K-values represent slow subsurface flow through loam. The watershed contributing area is divided into an “outer area” underlain by permafrost (which limits vertical infiltration depth), associated with index k = 0, and an “inner area” not underlain by permafrost (k = 1). The boundary between these areas approximately coincides with the early 1980s lake margin (Fig. 1b). The water flux from contributing area k, denoted as Qcontrib,k (m3 yr−1), is assumed to occur during the May–September snow-free season, as follows:
$$ {{\text{Q}}_{contrib,k}}\left( {{\theta_{w,k}}\left| {{y_k}} \right.} \right) = K\;{\theta_{w,k}}\;{y_k}\;{L_k}\;{t_{spy}}\left( {{\text{no sum on }}k} \right) $$
(3)
where subscript k denotes the outer (k = 0) or inner (k = 1) area, K = saturated hydraulic conductivity, θw,k = average of the maximum and minimum water-table slope during the season, yk = average of maximum and minimum aquifer thickness during the season, Lk = inner perimeter of contributing area, and tspy is a unit conversion factor (Table 4). Qcontrib,k is taken to be a function of θw,k (constant yk) for recharge of the gravel aquifer of the inner area, or yk (constant θw,k) for all other cases (Table 3). Qcontrib,k is calculated for the following conditions during 1984 and 2010: (1) minimum and maximum infiltration depths into the suprapermafrost aquifer (outer area), (2) no infiltration into the unfrozen gravel aquifer of the inner area, and (3) complete infiltration into the unfrozen gravel aquifer of the inner area (Table 3).
The flux Qcontrib to the lake during a season is derived by solving the water mass balance for each contributing area to obtain a dynamic steady-state, where the variation in water-table position is repeated from year to year:
$$ \left[ {{E_k}\left( {{y_k}\left| {{\theta_k}} \right.} \right) \cdot {A_{c,k}} + {Q_{contrib,k}}\left( {{y_k}\left| {{\theta_k}} \right.} \right)} \right]\delta {t_k} = \Delta {V_{in,k}} + P \cdot {A_{c,k}}\delta {t_k} $$
(4)
where Ek is soil evaporation as a function of depth to water table (Appendix; Table 3), Ac,k is the area of the contributing area, ΔVin,k equals the volume of snowmelt that infiltrates the aquifer of the assumed flowpath, and δtk equals the fraction of year (0 ≤ δtk ≤ 5/12) that satisfies dynamic steady state. The value of ΔVin,k is:
$$ \Delta {V_{in,k}} = {\text{SWE}} \cdot {A_{c,k}} + {Q_{contrib,k - 1}} \cdot \delta {t_{k - 1}} $$
(5)
where Qcontrib,k–1⋅δtk–1 is the volume of water exported from contributing area k–1 to area k during a season. The independent variable in Eq. 4 is either δtk, yk, or θw,k, depending on the aquifer and whether or not it desaturates during the season (see Table 3). For cases where the aquifer is predicted to remain saturated during a season, which occurs for the maximum infiltration cases of loam and fine sand in the outer area, the variable in Eq. 4 is yk and the value of δtk is set to the maximum value of 5/12 (Table 3). First, Eq. 4 is solved over the outer area to obtain the water volume exported to the inner area, Qcontrib,0⋅δt0, during a season, using Eq. 5, the constraint Qcontrib,–1 = 0, and relations in Table 3. The resulting water export, Qcontrib,0⋅δt0, is then inserted into Eq. 5 and used to solve Eq. 4 over the inner area (k = 1). Because the inner area is underlain by an unfrozen gravel aquifer, an additional step (“inner area water redistribution”) is taken where the sum of water fluxes reaching the lake (Qcontrib, SWE, P, and E) are laterally distributed over the lake and inner area gravel to produce a uniform height change in water level, which simulates reduced evaporation from the inner area as the lake level becomes lower.

Water flux to lake elevation relationship

The aforementioned water fluxes are related to lake surface elevation using the following mass-balance equation:
$$ \frac{{\Delta {h_l}}}{{\Delta t}} = {\text{SWE }} + \left( {P - E} \right) \cdot \delta {t_s} + \frac{1}{{{A_l}}}\sum {_i{Q_i}} $$
(6)
where Δhlt is the observed rate of change in lake surface elevation (m yr−1, positive upward), SWE is the meltwater from snow that has fallen on the lake, P is liquid precipitation falling on the lake per 5 month [m (5 month)−1], E is lake evaporation per 5 month [m (5 month)−1], δts is the unit conversion factor 5 month yr−1, Al is lake surface area (m2), and Qi is an indirect flux (m3 yr−1), as defined above (fluxes shown in Fig. 3).

Results

Permafrost distribution

Permafrost was not found at 19 out of 21 sites within the 1984 lake boundary, and was found at 0.4–2.5 m depth at 25 out of 36 sites outside of the 1984 lake boundary (Fig. 5a). Most of the ice-free sites outside of the 1984 lake boundary are located in the inlet and outlet channels.
Fig. 5

Maps showing a resistivity of subsurface (upper 10 m) from AEM interpretations and depth to ice from ground-based observations, and b AEM-based resistivities and lithology-ice interpretations along cross section AA’ through Twelvemile Lake, Yukon Flats, Alaska. Frozen material in b indicates permafrost. Vertical exaggeration 2.6 × in panel b. The boundary separating the outer (k = 0) and inner (k = 1) contributing areas is shown in a. See also Minsley et al. (2012)

These observations indicate that the early 1980s lake margin approximately separates watershed areas with and without permafrost, excluding the channels. This pattern is consistent with that from the AEM resistivity interpretation (Fig. 5), where resistivities greater than about 530 ohm-m (i.e., orange color in Fig. 5) generally reflect the presence of permafrost. Some of the relatively high resistivity values at non-permafrost, channel sites may be associated with the presence of gravel at relatively shallow depth (Jepsen et al. 2012). The AEM resistivity data also indicate the presence of an open talik below Twelvemile Lake (Minsley et al. 2012; Fig. 5b).

Based on these observations, the outer and inner contributing areas used for the Qcontrib calculation is defined to be the areas outside and inside, respectively, the 1984 lake boundary. Thus, the water flux to the lake during 1984 and 2010 associated with Qcontrib is given by Qcontrib,0⋅δt0 and Qcontrib,1⋅δt1, respectively. The modeled mean depth to permafrost (yp, Tables 3 and 4) in the outer area is taken to be the intermediate observed value of 1.5 m. The thickness of the gravel aquifer used for flowpath “infiltration to gravel” (y1, Tables 3 and 4) is set equal to 50 m (Fig. 5b). Lastly, segments 1 and 3 of groundwater flow (Lt,1 and Lt,3, Table 4) through an open talik (Qtalik) are assumed to pass through 100 m of silt in order to reach the approximate bottom of permafrost (Fig. 5b).

Climate and lake level observations

Twelvemile Lake began a steady decline in elevation (Δhlt) in the late 1970s to early 1980s at a rate of approximately 12 cm yr−1 (p < 0.001; Fig. 2d). During the preceding three decades, it increased in elevation at a rate of approximately 5.5 cm yr−1. Surface elevation trends for Buddy Lake are less significant than for Twelvemile Lake; however, both lakes show a trend reversal in the late 1970s to early 1980s (Fig. 2d). Twelvemile Lake attained its greatest level during the mid- to late-1970s when the surface elevation of Buddy Lake exceeded ∼132.8 m. This observation indicates a possible association between overflow of Buddy Lake, over a topographic threshold, and recharge of Twelvemile Lake, and is a topic of a separate, ongoing investigation.

May–September air temperatures have increased from a 1950–1980 average of 11.2°C, to a 1980–2010 average of 12.3 °C (Table 2), the strongest historical trends occurring for the months of May and July (Fig. 4a, b). This increase is similar to the 1.1 °C increase in summer air temperature in Fairbanks since 1974 (Barber et al. 2004). The computed PET and lake evaporation rates based on these air temperatures are 44 cm yr−1 between 1950 and 1980, and 46 cm yr−1 between 1980 and 2010. The 1950–1980 value is similar to a reported value of 46 cm yr−1 in Fairbanks during 1961 (Federer et al. 1996), and the change of 2 cm yr−1 between the periods 1950–1980 and 1980–2010 is consistent with the trend reported by Riordan et al. (2006). A 2-cm yr−1 increase in lake evaporation is 9 times lower than that needed to account for the observed 17.5 cm yr−1 decrease in lake mass balance around the early 1980s (change in Δhlt, Eq. 6).

Liquid precipitation (May–Sep) has averaged 10 cm yr−1 since the early 1950s (Table 2; Fig. 4d). Maximum SWE during recent times (2003–2010) has been approximately 10 cm on average, assuming a specific gravity of 0.21 for snow (Sturm et al. 2010, 2011; Table 2). Annual snowfall between 1980 and 2010 is 35 % lower than values over the preceding 30 years (Table 2; Fig. 4c), suggesting a substantial possible reduction in SWE during the last 6 decades.

Based on the mass balance components presented previously (Δhlt, SWE, P, E in Eq. 6), an average indirect flux of 22 cm yr−1 (lake area normalized) to Twelvemile Lake is required to account for its observed rate of change between 1950 and 2010. Therefore, a “significant” indirect flux is considered to be at least 11 cm yr−1. A decrease in indirect flux of 16 cm yr−1 is required to account for the observed rate of lake lowering beginning in the early 1980s; therefore, the water balance is considered to have “significant sensitivity” to an indirect flux change of 8 cm yr−1.

Lateral shallow groundwater flow across watershed boundary

Shallow, lateral groundwater flow across the watershed boundary is generally significant for threshold elevations above the approximate bottom of Twelvemile Lake (∼118 m asl)—for the 1984 outlet channel case if flow width is doubled (Fig. 6a). This indicates that a change in flow cross sectional area (threshold elevation and/or flow width) could produce a significant change in the recharge of Twelvemile Lake. The hydraulic conductivity of gravel can reach 10−1 m s−1 or greater (Freeze and Cherry 1979), which would increase flow rates in Fig. 6a by an order of magnitude. These results illustrate the types of flow rates that could occur for this path of groundwater flow.
Fig. 6

Predicted and observed quantities associated with shallow, lateral groundwater flow across the watershed boundary, over a permafrost table. a Predicted lateral flow rates, + (−) values represent flow to (from) the watershed. b Observed water-table elevations in the inlet (upper) and outlet (lower) channel of the Twelvemile Lake watershed during August 2011 (Jepsen et al. 2012)

One hypothesis to explain the lowering of Twelvemile Lake was increased subsurface discharge through the outlet channel in response to permafrost degradation. While plausible in 1984 for a flow width twice that assumed for Fig. 6a (Eqs. 1 and 6), the flow direction would have reversed around 1990 when the lake-surface elevation of Twelvemile had declined to ∼129 m asl (Fig. 2d), thus limiting further lake-level decline. Flow through the so-called outlet at present (2010) is predicted to be toward Twelvemile Lake (Fig. 6a), which is consistent with observed water-table elevations (Fig. 6b). The observed lake lowering of ∼2 m since 1990 is not consistent with the hypothesis of subsurface discharge through the outlet channel as a current mechanism of lake mass loss. However, significant subsurface flow from the watershed over other, unidentified thresholds should not be ruled out.

Significant fluxes are predicted for flow from Buddy to Twelvemile Lake through the inlet channel (Fig. 6a). However, observed water-table elevations suggest actual flow rates much lower than predicted, associated with a threshold elevation of about 131 m asl (Fig. 6b). This suggests that groundwater flow between these lakes is presently being impeded, for reasons unclear.

Vertical groundwater flow through open talik

Predicted groundwater flow-rates from Twelvemile Lake through an open talik to the Yukon River during 1984 are illustrated in Fig. 7a. Flow-rate magnitudes for all other endmember cases considered (see section Vertical groundwater flow through open talik, in Methods) during 1984 and 2010 (not shown) are within 40 % of the values in Fig. 7a. Flow from Buddy to Twelvemile Lake during 1984 would have been about half the value shown in Fig. 7b due to lower differences in lake elevation. These flow rates have insignificant sensitivity to the cross-sectional area of an open talik (Atalik) if the subpermafrost flowpath is through silt (Kt,2At,2 = 3 and 1 m3 s−1 in Fig. 7a, b, respectively). This suggests that open-talik development is not a likely cause of lake lowering if the subpermafrost flowpath follows silt. However, flow-rate sensitivity to Atalik is substantially increased by increasing the hydraulic conductance of the subpermafrost flowpath. For flow to and from the Yukon River during 1984, increasing Kt,2At,2 to 12 m3 s−1 would produce flow rates with high sensitivity to Atalik (Fig. 7a). This conductance could be provided by a layer of fine sand with a cross-sectional area (At,2) equal to 4 % of the lake area. Sand was logged between depths of 134 and 149 m in a borehole at Fort Yukon (Clark et al. 2009). In order for this layer to provide a Kt,2At,2 value of 12 m3 s−1, it would require a width of about 8 km, or about four lake diameters, during the early 1980s. Thus, development of an open talik as a significant mechanism of lake-mass loss may require substantial flow divergence below the permafrost into sparse sand layers, and strong interactions with regional groundwater flow.
Fig. 7

Predicted groundwater flow rates a from, and b to Twelvemile Lake through an open talik, as a function of talik cross-sectional area. Curve labels are the product of hydraulic conductivity and cross-sectional area along the subpermafrost flowpath (Kt,2At,2)

Lake recharge from snowmelt

Significant snowmelt recharge to Twelvemile Lake during 1984 from the watershed contributing area (Qcontrib) occurs for aquifers of snowpack and gravel (Fig. 8a, b). The snowpack aquifer represents rapid, overland flow of snowmelt to the lake. For flow through the other aquifers, evaporation removes nearly all water before it can reach the lake due to low values of hydraulic conductivity, low ground slope angle, and limited suprapermafrost-aquifer volume. With the exception of channels, gravel of the outer area is believed to generally be frozen; if this is true, the gravel case in Fig. 8b is unlikely. A reduction in SWE from 14 to 10 cm, assuming flow through snowpack, would produce a significant reduction (∼8 cm yr−1) in lake recharge (Fig. 8a). Alternatively, a change in flowpath of 5 cm of snowmelt from “snowpack” to “loam” would significantly reduce lake recharge (∼8 cm yr−1). These two endmember scenarios are developed as follows.
Fig. 8

Predicted water fluxes to Twelvemile Lake from the contributing-area slopes of the watershed (Qcontrib), as a function of the quantity of snowmelt infiltration into different materials. ab Values for 1984 lake geometry, “loam” values in a are less than 10−1 cm yr−1; Qcontrib values (ordinate) are given by Qcontrib,0⋅δt0 (Eq. 4). c Values for 2010 lake geometry, Qcontrib values are given by Qcontrib,1⋅δt1; the available water for snowmelt infiltration is from local snowmelt and the quantity exported from the outer contributing area: SWE + Qcontrib,0⋅δt0⋅(Ac,1)−1. d Predicted lake level change for 2010 lake geometry as a function of water fluxes to the lake (from panel c), with (solid) and without (dashed) lateral groundwater exchange with unfrozen gravel of the inner contributing area. The different labeled curves are for different values of the “Other Indirect” flux (× 104 m3 yr-1) required to maintain the pre-1984 lake in steady state

Reduced SWE scenario

The observed 1950–1980 lake level change of +5.5 cm yr−1 is predicted if lake evaporation = 44 cm yr−1, all snowmelt from 14 cm of SWE flows over frozen soil (through “snowpack” aquifer), and there is an additional flux—“other indirect flux” (OIF), assumed temporally constant—of +1.6 × 105 m3 yr−1 to the lake (Fig. 8a, Eq. 6). Beginning in the early 1980s, if lake evaporation increased to 46 cm yr−1, SWE decreased from 14 to 10 cm yr−1, and 4 cm of snowmelt began infiltrating into suprapermafrost loam, the lake level would have started declining by the observed rate of 12 cm yr−1 (Fig. 8a; Eq. 6). Later in 2010, the volume of SWE and contribution Qcontrib,0⋅δt0 from the outer contributing area (Qcontrib,0⋅δt0 from Fig. 8a for infiltration = 6 cm into “snowpack”) would have equaled 25 cm when distributed over the inner contributing area. Flow of this quantity of water through a snowpack or gravel aquifer would produce a rise, not fall, in lake level of ∼17 cm yr−1 assuming inner area redistribution (Fig. 8c, d), which is contrary to observation. If all 25 cm of available water infiltrated into loam of the inner area, the rate of lake lowering would be fairly close to the observed rate (8 cm yr−1; Fig. 8c, d). This illustrates that the observed, early-1980s trend reversal in lake-surface elevation could be attributed to a ∼30 % reduction in SWE only if the proportion of snowmelt that infiltrated into loam increased with progressive lake lowering (e.g., 40–100 % from 1984 to 2010, respectively).

Increased snowmelt infiltration scenario

The observed 1950–1980 lake level change of +5.5 cm yr−1 is predicted if lake evaporation = 44 cm yr−1, all snowmelt from 10 cm of SWE flows over frozen soil, and the OIF to the lake is 4.0 × 105 m3 yr−1 (Fig. 8a, Eq. 6). Beginning in the early 1980s, if lake evaporation increased to 46 cm yr−1, SWE remained at 10 cm yr−1, and 9 cm of snowmelt began infiltrating into suprapermafrost loam, the lake would have started declining by the observed rate of 12 cm yr−1 (Fig. 8a; Eq. 6). Later in 2010, the volume of SWE and contribution Qcontrib,0⋅δt0 would amount to 12 cm when distributed over the inner contributing area. During this year, for all flowpaths considered, the lake would be rising in level, not falling (Fig. 8c, d), as a result of the OIF to the lake basin and the reduced evaporation from the inner area in the presence of the lower lake level. To account for the observed rate of lake lowering, the value of the OIF to the inner area would need to decrease by ∼80 % (to 0.7 × 105 m3 yr−1; Fig. 8d). In summary, this scenario alone does not account for the observed change in lake level since the early 1980s.

The reduction in the sum of SWE and liquid precipitation (SWE + P) needed to account for the observed, early-1980s trend reversal in lake-surface elevation (+5.5 to −12 cm yr−1) is also considered. For this calculation (not shown), the ratio SWE:P is assumed fixed at 1:2. A 29 % reduction in SWE + P, from 28 to 20 cm yr−1, is required if all snowmelt flows over frozen soil (through “snowpack” aquifer), with about equal direct and indirect water flux reductions to the lake. Greater SWE + P reductions are needed if snowmelt follows slower flowpaths. A 29 % reduction seems unrealistically high considering observations in Table 2 and the statistically insignificant trends in annual precipitation reported for interior Alaska (Riordan et al. 2006; Wendler and Shulski 2009).

Discussion

The following mechanisms are demonstrated to be possible explanations for the lowering of Twelvemile Lake beginning in the early 1980s. Each mechanism is discussed below.
  1. (1)

    Changes in lateral, shallow (< ∼40 m) groundwater flow across the watershed boundary, through gravel

     
  2. (2)

    Changes in groundwater flow resulting from the development of an open talik, provided that subpermafrost flow is through sand, layers of which are sparse relative to lacustrine silt

     
  3. (3)

    A decrease in the mass of maximum-accumulation snowpacks in conjunction with increased infiltration of snowmelt into, and subsequent evaporation from, fine-grained sediment around the lake

     

The predicted 2 cm yr−1 increase in lake evaporation since the early 1980s is an order of magnitude lower than the observed 17.5 cm yr−1 change in mass balance, indicating that increased lake evaporation is not likely to be a primary mechanism. The length of the ice-covered season may have decreased by as much as 1–2 weeks since the late 1970s due to springtime warming (Brown et al. 2010; Foster et al. 2008). This would increase the duration of the open-water season, and hence lake evaporation (Woo 1980), by perhaps 10 %, which is still not adequate to be a likely primary mechanism.

Increased lateral, shallow groundwater flow from a lake’s watershed (mechanism 1) would occur if a lake overtopped the permafrost-table threshold at the watershed boundary, resulting in a type of shallow-subsurface flooding (Michel and van Everdingen 1994). This process would represent a subsurface analogue of lake drainage via overland flow through surface channels, as observed in other studies (Woo and Mielko 2007; Brewer et al. 1993; Mackay 1992), and may lead to sustained lake lowering if the rate of thermal erosion at the permafrost threshold could equal or exceed the rate of lake lowering (Marsh and Neumann 2001). Thawing of the transient layer (permafrost that freezes and thaws on decadal time scales; Shur et al. 2005) in gravelly material could facilitate an onset of this process. This mechanism was found to be potentially important despite the low topographic gradients of Yukon Flats because of the high hydraulic conductivity of gravel.

The requirement of high permeability in the subpermafrost aquifer for open-talik development (mechanism 2) to be an important mechanism of lake lowering results from the low hydraulic gradients in Yukon Flats, which are 2–3 orders of magnitude lower than gradients observed near Council, Alaska, where open taliks are an important mechanism for thermokarst pond drainage (Yoshikawa and Hinzman 2003). In the Yukon Flats, subpermafrost sand layers are minor in abundance relative to lacustrine silt (Williams 1962; Clark et al. 2009), suggesting that lake drainage through open taliks on a large scale in Yukon Flats may be limited by the permeability of the subpermafrost aquifer.

In regard to increased snowmelt infiltration (mechanism 3), previous studies have revealed a wide range of infiltration capacities of frozen soil (for reviews, see Ford and Bedford 1987; Dingman 1975). In environments where frozen soil has been found to prevent snowmelt infiltration and enhance overland flow (Woo and Steer 1983; Granger et al. 1984; Kane and Stein 1983; Kane 1980), which may be associated with relatively cold, moist soils, lake mass would have a high sensitivity to SWE. In contrasting environments where much or all snowmelt can infiltrate into frozen soil (Suzuki et al. 2006; Carey and Woo 1999; Marsh 1988), lake mass would have low sensitivity to SWE because of how little snowmelt reaches the lake. This would be especially true in areas of gentle topography and fine-grained soils such as Yukon Flats. Progressive lake lowering produces a gradient in the exposed land surface in vegetation and permafrost distribution. How this process affects soil moisture and snowmelt infiltration, and possible feedbacks on lake recharge, merits further study.

All of the plausible mechanisms for lake-level lowering identified in this study require the presence of certain geologic and/or permafrost conditions, known to display high spatial variability across the Yukon Flats. This finding is consistent with the high degree of non-uniformity observed in lake level changes in Yukon Flats (Rover et al. 2012; Riordan et al. 2006). Examples of these spatially varying characteristics include discontinuity of permafrost (Ferrians 1998), depth to the permafrost table, and SWE at maximum accumulation (Sturm et al. 2010, 2011). Further study combining spatial and temporal trends in lake-level change (e.g., Rover et al. 2012) and spatial variability in the relevant geological and permafrost characteristics identified in this study would provide a framework for understanding causes of lake level changes in Yukon Flats on a broader scale.

Processes not considered in this study, but which may also have notable effects on the water balance of lakes in Yukon Flats, include changes in intensity and recurrence of river flooding (Nakanishi and Dorava 1994), episodic flows over topographic thresholds (Woo and Mielko 2007), changes in the temporal distribution of rainfall which would influence runoff and evapotranspiration rates (e.g., Yuan et al. 2010), and beaver damming (Lewkowicz and Coultish 2004).

Conclusions

Mechanisms potentially responsible for the observed mass loss of lakes in Yukon Flats, Alaska, during the last three decades are identified through a site-specific (Twelvemile Lake) scoping analysis that tests lake-mass sensitivity to changes in flowpaths of snowmelt, maximum snow water equivalent (SWE), permafrost distribution, and evaporation. The observed 17.5 cm yr−1 reduction in lake mass balance since the early 1980s is an order of magnitude greater than predicted increases in lake evaporation due to May–September warming, indicating a greater importance of other mechanisms. The most important potential mechanisms are found to involve changes in lateral, shallow groundwater flow through gravel across the watershed boundary; groundwater flow through a sub-lacustrine open talik provided a subpermafrost flowpath through sand; and a substantial reduction in maximum SWE (e.g., ∼14–10 cm) in conjunction with increased infiltration of snowmelt into fine grained, unfrozen sediment mantling the lake basin. This list illustrates the influence of high permeability materials in controlling lake recharge in this region of low precipitation and low topographic gradient. Based on these findings, improved understanding about the spatial variability of lake level change in Yukon Flats may be obtained through more knowledge about the spatial variability in depth to permafrost, freeze-thaw interactions between the permafrost table and shallow groundwater flow through gravel, connectivity of open taliks to subpermafrost sand layers, and the effect of lake lowering on soil moisture and snowmelt infiltration. All of the plausible mechanisms for lake lowering identified in this study require specific geologic and/or permafrost conditions known to display high spatial variability across the Yukon Flats, a characteristic that is consistent with the high degree of non-uniformity observed in lake level changes in this region (Rover et al. 2012; Riordan et al. 2006).

Acknowledgements

Support for this study was provided by the USGS Mendenhall Research Fellowship Program, the National Research Program, and SERDP grant RC-2111. Technical assistance was provided by the following individuals: J. Abraham, L. Anderson, M.T. Jorgenson, J. Koch, J. O’Donnell, and J. Rover. We thank J. Koch and two anonymous reviewers for their helpful comments on the manuscript.

Copyright information

© Springer-Verlag (outside the USA) 2012

Authors and Affiliations

  • S. M. Jepsen
    • 1
  • C. I. Voss
    • 2
  • M. A. Walvoord
    • 1
  • J. R. Rose
    • 3
  • B. J. Minsley
    • 4
  • B. D. Smith
    • 4
  1. 1.US Geological SurveyDenver Federal CenterDenverUSA
  2. 2.US Geological SurveyMenlo ParkUSA
  3. 3.Yukon Flats National Wildlife RefugeUS Fish and Wildlife ServiceFairbanksUSA
  4. 4.US Geological SurveyDenver Federal CenterDenverUSA

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